Probing cosmic acceleration beyond the equation of state: Distinguishing between dark energy and modified gravity models
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If general relativity is the correct theory of physics on large scales, then there is a differential equation that relates the Hubble expansion function, inferred from measurements of angular diameter distance and luminosity distance, to the growth rate of large scale structure. For a dark energy fluid without couplings or an unusual sound speed, deviations from this consistency relationship could be the signature of modified gravity on cosmological scales. We propose a procedure based on this consistency relation in order to distinguish between some dark energy models and modified gravity models. The procedure uses different combinations of cosmological observations and is able to find inconsistencies when present. As an example, we apply the procedure to a universe described by a recently proposed 5-dimensional modified gravity model. We show that this leads to an inconsistency within the dark energy parameter space detectable by future experiments.
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By measuring growth of large-scale structure and luminosity and angular distances as functions of redshift via weak lensing, large-scale structure, supernovae, and cluster counting, LSST data can reveal whether recent cosmic acceleration is due to dark energy or modified gravity.
“By simultaneously measuring the growth of large-scale structure and luminosity and angular distances as functions of redshift ( via WL, LSS, SN, and cluster counting ) , LSST data can reveal whether the recent cosmic acceleration is due to dark energy or modi fi ed gravity”
From LSST: From Science Drivers to Reference Design and Anticipated Data Products (2019) · cites this paper as Ishak et al. 2006
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Constraints on a new post-general relativity cosmological parameter
Caldwell, R., Cooray, A., & Melchiorri, A. (2007) · Physical Review D · doi:10.1103/physrevd.76.023507 · Cited by 140 · see citing works
Large-scale tests of the Dvali-Gabadadze-Porrati model
Song, Y., Sawicki, I., & Hu, W. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.75.064003 · Cited by 137 · see citing works
The growth of matter perturbations inf(R) models
Gannouji, R., Moraes, B., & Polarski, D. (2009) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2009/02/034 · Cited by 132 · see citing works
Nonlinear evolution of the matter power spectrum in modified theories of gravity
Koyama, K., Taruya, A., & Hiramatsu, T. (2009) · Physical Review D · doi:10.1103/physrevd.79.123512 · Cited by 141 · see citing works
Matter perturbations in Galileon cosmology
Felice, A. D., Kase, R., & Tsujikawa, S. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.043515 · Cited by 130 · see citing works
Cuscuton cosmology: Dark energy meets modified gravity
Afshordi, N., Chung, D. J. H., Doran, M., & Geshnizjani, G. (2007) · Physical Review D · doi:10.1103/physrevd.75.123509 · Cited by 129 · see citing works
Parametrized post-Friedmann signatures of acceleration in the CMB
Hu, W. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.77.103524 · Cited by 127 · see citing works
Dispersion of growth of matter perturbations in f(R) gravity
Tsujikawa, S., Gannouji, R., Moraes, B., & Polarski, D. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.084044 · Cited by 126 · see citing works
Coupled dark matter-dark energy in light of near universe observations
Lopez-Honorez, L., Reid, B. A., Mena, O., Verde, L., & Jimenez, R. (2010) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2010/09/029 · Cited by 122 · see citing works
“It is well known that deviations from the simpler ΛCDM paradigm in the form of general relativity (GR) modifications can be constrained following two approaches: a) at the background evolution level as inconsistencies between the high-redshift and the low-redshift universe [51,52] and b) at the growth of perturbation…”
Density perturbations in general modified gravitational theories
Felice, A. D., Shinji Mukohyama, A., & Tsujikawa, S. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.023524 · Cited by 121 · see citing works
The phase-space view of f ( R ) gravity
de Souza, J. C. C., & Faraoni, V. (2007) · Classical and Quantum Gravity · doi:10.1088/0264-9381/24/14/006 · Cited by 120 · see citing works
Redshift space correlations and scale-dependent stochastic biasing of density peaks
Desjacques, V., & Sheth, R. K. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.81.023526 · Cited by 113 · see citing works
Pogosian, L., & Silvestri, A. (2016) · Physical Review D · doi:10.1103/physrevd.94.104014 · Cited by 112 · see citing works
Nonlinear interactions in a cosmological background in the Dvali-Gabadadze-Porrati braneworld
Koyama, K., & Silva, F. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.75.084040 · Cited by 110 · see citing works
Next generation redshift surveys and the origin of cosmic acceleration
Acquaviva, V., Hajian, A., Spergel, D. N., & Das, S. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.043514 · Cited by 109 · see citing works
Self-citationVelocities as a probe of dark sector interactions
Koyama, K., Maartens, R., & Song, Y. (2009) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2009/10/017 · Cited by 108 · see citing works
N -body simulations of DGP and degravitation theories
Khoury, J., & Wyman, M. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.064023 · Cited by 108 · see citing works
“Much effort has been devoted recently to confronting DGP with cosmological observations [7, 8, 9, 10, 11, 12, 13, 14, 15, 16], most of which pertains to the self-accelerated or unstable branch.”
BackgroundGrowth Rate of Cosmological Perturbations at z∼0.1 from a New Observational Test
Feix, M., Nusser, A., & Branchini, E. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.011301 · Cited by 104 · see citing works
Growth factor parametrization and modified gravity
Gong, Y. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.123010 · Cited by 106 · see citing works
Behavior of f(R) gravity in the solar system, galaxies, and clusters
Zhang, P. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.024007 · Cited by 101 · see citing works
Do we have any hope of detecting scattering between dark energy and baryons through cosmology?
Vagnozzi, S., Visinelli, L., Mena, O., & Mota, D. F. (2020) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staa311 · Cited by 95 · see citing works
Observational signatures of Jordan–Brans–Dicke theories of gravity
Acquaviva, V., & Verde, L. (2007) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2007/12/001 · Cited by 95 · see citing works
Is modified gravity required by observations? An empirical consistency test of dark energy models
Wang, S., Hui, L., May, M., & Haiman, Z. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.063503 · Cited by 92 · see citing works
Investigating dark energy experiments with principal components
Crittenden, R., Pogosian, L., & Zhao, G.-B. (2009) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2009/12/025 · Cited by 91 · see citing works
“J C A P 1 2 ( 2 0 0 9 ) 0 2 5 Another important question is whether the constraints from measures of w(z) coming from the background expansion (CMB, SN) are consistent with those arising from the growth of perturbations (correlations, weak lensing), since inconsistencies could potentially indicate a breakdown of gener…”
BackgroundThe growth of matter perturbations in some scalar–tensor DE models
Gannouji, R., & Polarski, D. (2008) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2008/05/018 · Cited by 86 · see citing works
Weak lensing, dark matter and dark energy
Huterer, D. (2010) · General Relativity and Gravitation · doi:10.1007/s10714-010-1051-z · Cited by 70 · see citing works
Testing general relativity at cosmological scales: Implementation and parameter correlations
Dossett, J. N., Ishak, M., & Moldenhauer, J. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.123001 · Cited by 83 · see citing works
Self-citationN -body simulations of alternative gravity models
Stabenau, H. F., & Jain, B. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.74.084007 · Cited by 83 · see citing works
Consistency test of general relativity from large scale structure of the universe
Song, Y., & Koyama, K. (2009) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2009/01/048 · Cited by 81 · see citing works
Cosmological discordances. II. Hubble constant, Planck and large-scale-structure data sets
Lin, W., & Ishak, M. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.083532 · Cited by 79 · see citing works
“In addition to parameter constraint analyses, we are witnessing an interest from the scientific literature into consistency tests between various data sets [1–17].”
BackgroundMethodSelf-citationThe cosmological constant and dark energy in braneworlds
Koyama, K. (2007) · General Relativity and Gravitation · doi:10.1007/s10714-007-0552-x · Cited by 79 · see citing works
Probing the cosmographic parameters to distinguish between dark energy and modified gravity models
Wang, F. Y., Dai, Z.-G., & Qi, S. (2009) · Astronomy and Astrophysics · doi:10.1051/0004-6361/200911998 · Cited by 78 · see citing works
Cosmological constraints from COMBO-17 using 3D weak lensing
Kitching, T., Heavens, A., Taylor, A. N., Brown, M. D., Meisenheimer, K., Wolf, C., Gray, M. E., & Bacon, D. (2007) · Monthly Notices of the Royal Astronomical Society · doi:10.1111/j.1365-2966.2007.11473.x · Cited by 78 · see citing works
“To determine whether dark energy is a field or a manifesta- tion of of modified gravity (e.g. Ishak et al., 2006), one needs methods can probe the expansion history of Universe, as is the case with the geometric shear-ratio analysis, or both the expansion history and the growth of structure as is…”
MethodConsistent perturbations in an imperfect fluid
Sawicki, I., Saltas, I. D., Amendola, L., & Kunz, M. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/01/004 · Cited by 77 · see citing works
“It was quickly understood that whereas the background expansion history can be indistinguishable between various classes of these models, the evolution of dark-matter perturbations can differ significantly and therefore formation of large-scale structure provides the key to understanding the role played by these theor…”
BackgroundTests of gravity from imaging and spectroscopic surveys
Guzik, J., Jain, B., & Takada, M. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.81.023503 · Cited by 77 · see citing works
A perturbative approach to the redshift space power spectrum: beyond the Standard Model
Bose, B., & Koyama, K. (2016) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2016/08/032 · Cited by 73 · see citing works
Cosmology with the Large Synoptic Survey Telescope: an overview
Zhan, H., & Tyson, T. (2018) · Reports on Progress in Physics · doi:10.1088/1361-6633/aab1bd · Cited by 73 · see citing works
Spherical collapse in f(R) gravity
Borisov, A., Jain, B., & Zhang, P. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.063518 · Cited by 72 · see citing works
Lin, W., & Ishak, M. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.023532 · Cited by 70 · see citing works
Self-citationTheoretical priors on modified growth parametrisations
Song, Y.-S., Hollenstein, L., Caldera-Cabral, G., & Koyama, K. (2010) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2010/04/018 · Cited by 69 · see citing works
Charged wormholes in f(R,T)-extended theory of gravity
Moraes, P. H. R. S., de Paula, W., & Correa, R. A. C. (2019) · International Journal of Modern Physics D · doi:10.1142/s0218271819500986 · Cited by 69 · see citing works
Constraining modified gravity and growth with weak lensing
Thomas, S. A., Abdalla, F., & Weller, J. (2008) · Monthly Notices of the Royal Astronomical Society · doi:10.1111/j.1365-2966.2009.14568.x · Cited by 51 · see citing works
“…these include parameterising the relationship between the two metric potentials (φ and ψ) and/or quantifying any modification to the Poisson equation (E.g. Amendola et al. (2007), Hu & Sawicki (2007), Ishak et al. (2006), Jain & Zhang (2007), Daniel et al. (2008) and Bertschinger & Zukin (2008)).”
BackgroundTidal alignments as a contaminant of redshift space distortions
Hirata, C. M. (2009) · Monthly Notices of the Royal Astronomical Society · doi:10.1111/j.1365-2966.2009.15353.x · Cited by 68 · see citing works
“…relativity rather than a new contribution to the c© 0000 RAS cosmic energy budget have motivated studies of the growth of structure, as it is impossible to distinguish these models from dark energy using distance information alone (e.g. Ishak et al. 2006; Song & Percival 2008; Song & Koyama 2009).”
MethodDo observations offer evidence for cosmological-scale extra dimensions?
Afshordi, N., Geshnizjani, G., & Khoury, J. (2009) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2009/08/030 · Cited by 69 · see citing works
“The confrontation of its cosmological predictions with observations has been the subject of much literature since its advent [22, 23, 24, 25, 26, 27, 28, 29, 30].”
Zhan, H., Knox, L., & Tyson, J. A. (2009) · The Astrophysical Journal · doi:10.1088/0004-637x/690/1/923 · Cited by 67 · see citing works
How close can an inhomogeneous universe mimic the concordance model?
Dunsby, P., Goheer, N., Osano, B., & Uzan, J. (2010) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2010/06/017 · Cited by 64 · see citing works
“Since γ can be measured from galaxy redshift surveys [47], thanks to the redshift distortion [46], it was argued that the value of the parameter γ offers a test of general relativity [40].”
BackgroundMethodModel-independent constraints on the cosmic opacity
Holanda, R. F. L., Carvalho, J. C., & Alcaniz, J. S. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/04/027 · Cited by 62 · see citing works
The growth of matter perturbations in some scalar-tensor DE modelsPreprint
Gannouji, R., & Polarski, D. (2008) · Cited by 62 · see citing works
Amin, M. A., Wagoner, R. V., & Blandford, R. D. (2008) · Monthly Notices of the Royal Astronomical Society · doi:10.1111/j.1365-2966.2008.13474.x · Cited by 61 · see citing works
“(1) Considerable effort has been made in constructing models that fall into the above mentioned categories and more recently in finding ways to distinguish between them (for example see Lue et al. 2004; Ishak et al. 2006; Bludman 2007; Zhang et al. 2007; Huterer & Linder 2007).”
BackgroundTesting the dark energy consistency with geometry and growth
Ruiz, E. J., & Dragan Huterer, A. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.91.063009 · Cited by 59 · see citing works
Consistent cosmological modifications to the Einstein equations
Skordis, C. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.79.123527 · Cited by 58 · see citing works
Perturbations of the self-accelerated Universe
Deffayet, C., Gabadadze, G., & Iglesias, A. (2006) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2006/08/012 · Cited by 58 · see citing works
Spatial curvature and cosmological tests of general relativity
Dossett, J. N., & Ishak, M. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.86.103008 · Cited by 55 · see citing works
Self-citationTests of general relativity on astrophysical scales
Uzan, J. (2010) · General Relativity and Gravitation · doi:10.1007/s10714-010-1047-8 · Cited by 59 · see citing works
Remarks on the Formulation of the Cosmological Constant/Dark Energy Problems
Ishak, M. (2007) · Foundations of Physics · doi:10.1007/s10701-007-9175-z · Cited by 55 · see citing works
Self-citationLarge-scale structure formation with massive neutrinos and dynamical dark energy
Upadhye, A., Biswas, R., Pope, A., Heitmann, K., Habib, S., Finkel, H., & Frontiere, N. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.89.103515 · Cited by 54 · see citing works
Self-citationGrowth factor parametrization in curved space
Gong, Y., Ishak, M., & Wang, A. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.023002 · Cited by 52 · see citing works
Self-citationEvolution of galaxy bias, generalized
Hui, L., & Parfrey, K. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.77.043527 · Cited by 37 · see citing works
Modified gravity constraints from the full shape modeling of clustering measurements from DESI 2024
Ishak, M., Pan, J., Calderón, R., Lodha, K., Valogiannis, G., Avilés, A., Niz, G., Yi, L., Zheng, C., García-Quintero, C., et al. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/09/053 · Cited by 49 · see citing works
Self-citationRemarks on the formulation of the cosmological constant/dark energy problems
Ishak, M. (2005) · CERN Document Server (European Organization for Nuclear Research) · Cited by 49 · see citing works
Self-citationZhao, G. B., Xia, J. Q., Feng, B., & Zhang, X. (2006) · CERN Document Server (European Organization for Nuclear Research) · Cited by 49 · see citing works
Towards precision constraints on gravity with the Effective Field Theory of Large-Scale Structure
Bose, B., Koyama, K., Lewandowski, M., Vernizzi, F., & Winther, H. A. (2018) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2018/04/063 · Cited by 57 · see citing works
Dragan Huterer, A. (2023) · The Astronomy and Astrophysics Review · doi:10.1007/s00159-023-00147-4 · Cited by 48 · see citing works
“Comparing measurements of geometric quantities to those describing the growth of structure is a particularly promising stress-test of the cosmological model (Zhang et al. 2005; Bernstein and Jain 2004; Ishak et al. 2006; Knox et al. 2006; Bertschinger 2006; Huterer and Linder 2007).”
Contiguous redshift parameterizations of the growth index
Ishak, M., & Dossett, J. N. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.043004 · Cited by 48 · see citing works
Self-citationZHAO, G.-B., XIA, J.-Q., ZHANG, X.-M., & FENG, B. (2007) · International Journal of Modern Physics D · doi:10.1142/s0218271807010717 · Cited by 48 · see citing works
- Authors
- Ishak, M., Upadhye, A., & Spergel, D. N.
- Affiliations
- The University of Texas at Dallas (US)
- Princeton University (US)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2006-08-15
- Volume
- 74
- Issue
- 4
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2044422425
- Cited by
- 239
- References
- 55
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 2 · 2023: 7 · 2022: 3 · 2021: 6 · 2020: 3 · 2019: 7 · 2018: 7 · 2017: 8 · 2016: 17 · 2015: 6 · 2014: 11 · 2013: 10 · 2012: 10
- FWCI
- 15.87
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (acceptedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Dark Matter and Cosmic Phenomena
- Keywords
- cosmic acceleration, dark energy, modified gravity, consistency relations, Hubble expansion, angular diameter distance, luminosity distance, large-scale structure growth, dark energy equation of state, sound velocity, five-dimensional gravity
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